If we achieve sentience using mutable hardware, will it be possible to make a copy of that "brain" and its active state?
Theoretically, there shouldn't be a problem copying either of the artificial brains in any state. 

Difficulty in measuring a state doesn't seem to really be a problem until you get down to the quantum level, where the means of measurement affect the state.

The configuration of the artificial brains, including pathway structures and states, should be reducible to a single string, which could then be used to reconfigure the artificial brain the information is being copied to.



Definitely look into the concept of a Turing Machine and Universal Turing Machine.